$75$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $90$ less than $4$ times the number of away team fans. How many home team and away team fans attended the game?
Answer: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 75}$ ${x = 4y-90}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${4y-90}$ for $x$ in the first equation. ${(4y-90)}{+ y = 75}$ Simplify and solve for $y$ $ 4y-90 + y = 75 $ $ 5y-90 = 75 $ $ 5y = 165 $ $ y = \dfrac{165}{5} $ ${y = 33}$ Now that you know ${y = 33}$ , plug it back into ${x = 4y-90}$ to find $x$ ${x = 4}{(33)}{ - 90}$ $x = 132 - 90$ ${x = 42}$ You can also plug ${y = 33}$ into ${x+y = 75}$ and get the same answer for $x$ ${x + }{(33)}{= 75}$ ${x = 42}$ There were $42$ home team fans and $33$ away team fans.